Assignee is who holds the work. EMPTY MEANS UNHELD, which is what makes the issue claimable: claiming one already held by someone else is refused with 409 rather than quietly taken.
Number is the issue's number on that board, from 1 and monotonic there. Unique per board, never across the org — so it addresses an issue only together with Project.
Status is the board column: backlog, todo, in_progress, done or canceled. Claiming moves backlog and todo to in_progress and leaves the other three where they are.
URL is the row's external anchor — its extRef — which is a link only when the feeder sent one. A mirrored GitHub issue carries "github:owner/repo#123" and an agent's PR row carries the pushed branch. Empty for a row opened here.